I agree on the first point. I found that scene to be heartwrenching. And while it does change my opinion of her, it really makes me like her more as a character. I like it when good people do shitty things for what they believe to be the right (but ultimately wrong) reasons. To me, that's the core of great character development. It's Xander telling Buffy to kill Angel.Well, what Burnham did to Spock was terrible. I see her distorted rationale but I won't look at the character the same way ever again.
Also, Mary Sues don't tell the most popular character in the franchise to fuck off. Just throwing that out there.